Peter Kotelenez

Stochastic Ordinary and Stochastic Partial Differential Equations (eBook, PDF)

Transition from Microscopic to Macroscopic Equations

• Format: PDF

Produktbeschreibung

Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail. Coverage first describes the transition from the microscopic equations to the mesoscopic equations. It then covers a general system for the positions of the large particles.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 459
• Erscheinungstermin: 5. Dezember 2007
• Englisch
• ISBN-13: 9780387743172
• Artikelnr.: 37288405

Inhaltsangabe

From Microscopic Dynamics to Mesoscopic Kinematics.- Heuristics: Microscopic Model and Space-Time Scales.- Deterministic Dynamics in a Lattice Model and a Mesoscopic (Stochastic) Limit.- Proof of the Mesoscopic Limit Theorem.- Mesoscopic A: Stochastic Ordinary Differential Equations.- Stochastic Ordinary Differential Equations: Existence, Uniqueness, and Flows Properties.- Qualitative Behavior of Correlated Brownian Motions.- Proof of the Flow Property.- Comments on SODEs: A Comparison with Other Approaches.- Mesoscopic B: Stochastic Partial Differential Equations.- Stochastic Partial Differential Equations: Finite Mass and Extensions.- Stochastic Partial Differential Equations: Infinite Mass.- Stochastic Partial Differential Equations:Homogeneous and Isotropic Solutions.- Proof of Smoothness, Integrability, and Itô's Formula.- Proof of Uniqueness.- Comments on Other Approaches to SPDEs.- Macroscopic: Deterministic Partial Differential Equations.- Partial Differential Equations as a Macroscopic Limit.- General Appendix.

Rezensionen

From the reviews:

"This book treats the transition from microscopic to macroscopic equations for particle systems. ... Peter Kotelenez ... has written a monograph in which he rigorously constructs the theory of correlated Brownian motion in interacting particle systems. ... Researchers working on interacting particle systems and probability theory will definitely find this book very useful." (J. Dubbeldam, Kwantitatieve Methoden, Issue R11, 2008)

"This interesting book treats in detail stochastic partial differential equations (SPDEs) describing mass distribution of particles. The book introduces in an essentially self-contained manner the author's research on the evolution of large particles interacting with an environment consisting, for instance, of small particles. ... To help the reader, the book devotes four of the fourteen chapters to the more lengthy proofs of some theorems. ... the reviewer recommends this book to any researcher interested in SPDEs." (Carlos M. Mora González, Mathematical Reviews, Issue 2009 h)

"The monography under review presents mathematical models for physical dynamical systems of particle and mass evolution on different levels ... . Extremely helpful are the excellent summaries at the beginning of each chapter. ... This monography is a highly impressive result of many years of concise scientific studies on SODEs, SPDEs and mathematical physics. I warmly recommend this book for scientific and personal enlightenment to graduate students ... as well as to mathematical scientists in mathematical physics, theoretical physics and mathematical biology." (Michael Högele, Zentralblatt MATH, Vol. 1159, 2009)